Question

If 9 is added to the numerator and denominator of a tion, the tion becomes 4/5, and if 8 is subtracted from its numerator and denominator, it becomes 2/3. What is the tion?

- (A) 2/3
- (B) 5/7
- (C) 3/4
- (D) 4/5

Answer 1

To find the fraction, set up a system of equations using the given information and solve for the values of a and b. The fraction is 17/15.

Step-by-step explanation:

To find the fraction, let's start by setting up a system of equations based on the given information:

Let the fraction be represented as a/b.

From the first statement, we have (a+9)/(b+9) = 4/5.

From the second statement, we have (a-8)/(b-8) = 2/3.

Now we can solve this system of equations to find the values of a and b.

First, we can cross-multiply in the first equation to get 5(a+9) = 4(b+9).

Simplifying, we get 5a + 45 = 4b + 36.

Similarly, cross-multiplying in the second equation gives us 3(a-8) = 2(b-8).

Simplifying, we get 3a - 24 = 2b - 16.

We now have a system of linear equations which can be solved to find the values of a and b. Solving this system, we find that a = 17 and b = 15.

Therefore, the fraction is 17/15.